Sunday, January 18, 2015

Before we start, I'd like to thank listeners katenmkate and EdB, who recently posted nice reviews on iTunes. I'd also like to welcome our many new listeners-- from the hits on the Facebook page, I'm guessing a bunch of you out there just got new smartphones for Xmas and started listening to podcasts. Remember, posting good reviews on iTunes helps spread the word about Math Mutation, as well as motivating me to get to work on the next episode.

Anyway, on to today's topic. We often think of mathematical history as something that happened far in the past, rather than something that is still going on. This is understandable to some degree, as until you get to the most advanced level of college math classes, you generally are learning about discoveries and theorems proven centuries ago. But even since this podcast began in 2007, the mathematical world has not stood still. In particular, way back in episode 12, we discussed the strange case of Grigori Perelman, the Russian genius who had refused the Fields Medal, widely viewed as math's equivalent of the Nobel Prize. Perelman is still alive, and his saga has just continued to get more bizarre.

As you may recall, Grigori Perelman was the first person to solve one of the Clay Institute's celebrated "Millennium Problems", a set of major problems identified by leading mathematicians in the year 2000 as key challenges for the 21st century. Just two years later, Perelman posted a series of internet articles containing a proof of the Poincare Conjecture, a millennium problem involving the shapes of certain multidimensional spaces. But because he had posted it on the internet instead of in a refereed journal, there was some confusion about when or how he would qualify for the prize. And amid this controversy, a group of Chinese mathematicians published a journal article claiming they had completed the proof, apparently claiming credit for themselves for solving this problem. The confusion was compounded by the fact that so few mathematicians in the world could fully understand the proof to begin with. Apparently all this bickering left a bitter taste in Perelman's mouth, and even though he was selected to receive the Fields Medal, he refused it, quit professional mathematics altogether, and moved back to Russia to quietly live with his mother.

That was pretty much where things stood at the time we discussed Perelman in podcast 12. My curiosity about his fate was revived a few months ago when I read Masha Gessen's excellent biography of Perlman, "Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century". It gives a great overview of Perelman's early life, where he became a superstar in Russian math competitions but still had to contend with Soviet anti-semitism when moving on to university level. It also continues a little beyond the events of 2006, describing a somewhat happy postscript: eventually the competing group of Chinese mathematicians retitled their paper " Hamilton–Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture", explicitly removing any attempt to claim credit for the proof, and recasting their contribution as merely providing a more readable explanation of Perelman's proof. Sadly, this did not cause Perelman to rejoin the mathematical community: he has continued to live in poverty and seclusion with his mother, remaining retired from mathematics and refusing any kind of interviews with the media.

As you would expect, this reclusiveness just served to pique the curiosity of the world media, and there were many attempts to get him to give interviews or return to public life. Even when researching her biography, Masha Gessen was unable to get an interview. In 2010, the Clay institute finally decided to officially award him the million dollar prize for solving the Poincare Conjecture There had been some concern that his refusal to publish in a traditional journal would disqualify him for the prize, but the Institute seemed willing to modify the rules in this case. Still, Perelman refused to accept the prize or rejoin the mathematical community. He claimed that this was partially because he thought Richard Hamilton, another mathematician whose work he had built upon for the proof, was just as deserving as he was. He also said that "the main reason is my disagreement with the organized mathematical community. I don't like their decisions, I consider them unjust." Responding to a persistent reporter through the closed door of his apartment, he later clarified that he didn't want "to be on display like an animal in a zoo." Even more paradoxically, he added "I'm not a hero of mathematics. I'm not even that successful." Perhaps he just holds himself and everyone else to impossibly high standards.

Meanwhile, Perelman's elusiveness to the media has continued. In 2011 a Russian studio filmed a documentary about him, again without cooperation or participation from Perelman himself. A Russian journalist named Alexander Zabrovsky claimed later that year to have successfully interviewed Perelman and published a report, but experienced analysts, including biographer Masha Gessen, poked that report full of holes, pointing out various unlikely statements and contradictions. One critic provided the amusing summary "All those thoughts about nanotechnologies and the ideas of filling hollowness look like rabbi's thoughts about pork flavor properties." A more believable 2012 article by journalist Brett Forrest describes a brief, and rather unenlightening, conversation he was able to have with Perelman after staking out his apartment for several days and finally catching him while the mathematician and his mother were out for a walk.

Probably the most intriguing possibility here is that Perelman has not actually abandoned mathematics, but has merely abandoned the organized research community, and is using his seclusion to quietly work on the problems that truly interest him. Fellow mathematician Yakov Eliashberg claimed in 2007 that Perelman had privately confided that he was working on some new problems, but did not yet have any results worth reporting. Meanwhile, Perelman continues to ignore the world around him, as he and his mother quietly live in their small apartment in St Petersburg, Russia. Something tells me that this not quite the end of the Perelman story, or of his contributions to mathematics.

Note that this podcast is intended mainly for audio consumption, so you will not see the numerous illustrations & diagrams you would find at most math sites, though these are linked in the show notes whenever possible.

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